McMullen's simplifies his original proof of the g-theorem in [1]} by working over the ring of Minkowski weights. One technical difficulty is that we have to actually give a ring structure to \(\Omega (P)\) , to define, compatible with \(\phi \) , a way to multiply weights. This is a delicate part of [1]}, but ultimately McMullen gives a simplification of the proof of the g-theorem by replacing \(\Pi (P)\)  with \(\Omega (P)\) . He writes “The reader who wishes to work through the proof of the g-theorem in the light of the weight algebra can effectively discard much of [3]}".
